decision trees
DESCRIPTION
PPTTRANSCRIPT
AN INTRODUCTION TO
DECISION TREES
Prepared for:CIS595 Knowledge Discovery and Data MiningProfessor Vasileios Megalooikonomou
Presented by:Thomas Mahoney
Learning Systems
Learning systems consider Solved cases - cases assigned to a class
Information from the solved cases - general decision rules Rules - implemented in a model Model - applied to new cases Different types of models - present their results in various
forms
Linear discriminant model - mathematical equation (p = ax1 + bx2 + cx3 + dx4 + ex5).
Presentation comprehensibility
Data Classification and Prediction
Data classification classification prediction
Methods of classification decision tree induction Bayesian classification backpropagation association rule mining
Data Classification and Prediction
Method creates model from a set of training data individual data records (samples, objects,
tuples) records can each be described by its
attributes attributes arranged in a set of classes supervised learning - each record is assigned
a class label
Data Classification and Prediction
Model form representations mathematical formulae classification rules decision trees
Model utility for data classification degree of accuracy predict unknown outcomes for a new (no-test) data
set classification - outcomes always discrete or nominal
values regression may contain continuous or ordered
values
Description of Decision Rules or Trees
Intuitive appeal for users Presentation Forms
“if, then” statements (decision rules) graphically - decision trees
What They Look Like Works like a flow chart Looks like an upside down tree Nodes
appear as rectangles or circles represent test or decision
Lines or branches - represent outcome of a test
Circles - terminal (leaf) nodes Top or starting node- root node Internal nodes - rectangles
An Example Bank - loan application Classify application
approved class denied class
Criteria - Target Class approved if 3 binary attributes have certain value: (a) borrower has good credit history (credit rating in excess of some
threshold) (b) loan amount less than some percentage of collateral value (e.g.,
80% home value) (c) borrower has income to make payments on loan
Possible scenarios = 32 = 8 If the parameters for splitting the nodes can be adjusted, the number
of scenarios grows exponentially.
How They Work Decision rules - partition sample of data Terminal node (leaf) indicates the class assignment Tree partitions samples into mutually exclusive groups One group for each terminal node All paths
start at the root node end at a leaf
Each path represents a decision rule joining (AND) of all the tests along that path separate paths that result in the same class are disjunctions (ORs)
All paths - mutually exclusive for any one case - only one path will be followed false decisions on the left branch true decisions on the right branch
Disjunctive Normal Form
Non-terminal node - model identifies an attribute to be tested test splits attribute into mutually exclusive
disjoint sets splitting continues until a node - one class
(terminal node or leaf) Structure - disjunctive normal form
limits form of a rule to conjunctions (adding) of terms
allows disjunction (or-ing) over a set of rules
Geometry Disjunctive normal form Fits shapes of decision boundaries between classes Classes formed by lines parallel to axes Result - rectangular shaped class regions
Binary Trees Characteristics
two branches leave each non-terminal node
those two branches cover outcomes of the test
exactly one branch enters each non-root node
there are n terminal nodes there are n-1 non-terminal nodes
Nonbinary Trees Characteristics
two or more branches leave each non-terminal node
those branches cover outcomes of the test
exactly one branch enters each non-root node
there are n terminal nodes there are n-1 non-terminal nodes
Goal
Dual goal - Develop tree that is small classifies and predicts class with accuracy
Small size a smaller tree more easily understood smaller tree less susceptible to overfitting large tree less information regarding
classifying and predicting cases
Rule Induction
Process of building the decision tree or ascertaining the decision rules tree induction rule induction induction
Decision tree algorithms induce decision trees recursively from the root (top) down - greedy approach established basic algorithms include ID3 and
C4.5
Discrete vs. Continuous Attributes Continuous variables attributes - problems for
decision trees increase computational complexity of the task promote prediction inaccuracy lead to overfitting of data
Convert continuous variables into discrete intervals “greater than or equal to” and “less than” optimal solution for conversion difficult to determine discrete intervals ideal
• size• number
Making the Split Models induce a tree by recursively
selecting and subdividing attributes random selection - noisy variables inefficient production of inaccurate trees
Efficient models examine each variable determine which will improve accuracy of
entire tree problem - this approach decides best split
without considering subsequent splits
Evaluating the Splits Measures of impurity or its inverse, goodness reduce impurity or degree of randomness at each node popular measures include:
Entropy Function - pj log pj j
Gini Index 1 - p2
j
j
Twoing Rule k
(TL /n) * (TR /n) * ( Li TL - RiTR)2
i=1
Overfitting
Error rate in predicting the correct class for new cases overfitting of test data very low apparent error rate high actual error rate
Optimal Size Certain minimal size smaller tree
higher apparent error rate lower actual error rate
Goal identify threshold minimize actual error rate achieve greatest predictive accuracy
Ending Tree Growth Grow the tree until
additional splitting produces no significant information gain
statistical test - a chi-squared test problem - trees that are too small only compares one split with the next
descending split
Pruning Grow large tree
reduce its size by eliminating or pruning weak branches step by step
continue until minimum true error rate Pruning Methods
reduced-error pruning divides samples into test set and training set training set is used to produce the fully expanded
tree tree is then tested using the test set weak branches are pruned stop when no more improvement
Pruning Resampling
5 - fold cross-validation 80% cases used for training; remainder for
testing Weakest-link or cost-complexity pruning
trim weakest link ( produces the smallest increase in the apparent error rate)
method can be combined with resampling
Variations and Enhancements to Basic Decision Trees Multivariate or Oblique Trees
CART-LC - CART with Linear Combinations
LMDT - Linear Machine Decision Trees SADT - Simulated Annealing of Decision
Trees OC1 - Oblique Classifier 1
Evaluating Decision Trees
Method’s Appropriateness Data set or type Criteria
accuracy - predict class label for new data scalability
• performs model generation and prediction functions• large data sets• satisfactory speed
robustness • perform well despite noisy or missing data
intuitive appeal • results easily understood• promotes decision making
Decision Tree Limitations
No backtracking local optimal solution not global optimal
solution lookahead features may give us better trees
Rectangular-shaped geometric regions in two-dimensional space
• regions bounded by lines parallel to the x- and y- axes
some linear relationships not parallel to the axes
Conclusions Utility
analyze classified data produce accurate and easily understood classification
rules with good predictive value
Improvements Limitations being addressed multivariate discrimination - oblique trees data mining techniques
Bibliography
A System for Induction of Oblique Decision Trees, Sreerama K. Murthy, Simon Kasif, Steven Salzberg, Journal of Artificial Intelligence Research 2 (1994) 1-32.
Automatic Construction of Decision Trees from Data: A Multi-Disciplinary Survey, Sreerama K. Murthy, Data Mining and Knowledge Discovery, 2. 345-389 (1998) Kluwer Academic Publishers.
Classification and Regression Trees, Leo Breiman, Jerome Friedman, Richard Olshen and Charles Stone, 1984, Wadsworth Int. Group.
Computer Systems That Learn, Sholom M. Weiss and Casimer A. Kulikowski, 1991, Morgan Kaufman.
Data Mining, Concepts and Techniques, Jiawei Han and Micheline Kamber, 2001, Morgan Kaufman.
Introduction to Mathematical Techniques in Pattern Recognition, Harry C. Andrews, 1972, Wiley-Interscience.
Machine Learning, Tom M. Mitchell, 1997, McGraw-Hill.